Westwood beat Ross Fisher by two holes and Villegas defeated Jeev Milkha Singh 3 up at the Finca Cortesin golf club. All four players in Group D have two points.
Group C also has four players with two points from two matches after Stenson held off former Masters champion Angel Cabrera 2 up, while McIlroy kept his chances alive with a two-hole victory over Simon Dyson.
Cabrera, who leads Group C on hole difference, can qualify for the semifinals with a win over Dyson later on Friday. Singh leads Group D by the same three-hole advantage and can play Saturday by beating Fisher.
American player Anthony Kim only needs to halve his match with Scott Strange later Friday to win Group A. Retief Goosen will need a big win over the already eliminated Paul Casey to maintain his hopes of advancing.
Oliver Wilson can claim Group B's place in the semifinals by halving against Robert Allenby.
Down after the first hole, Westwood rallied with three straight birdies before an eagle at the par-5 fifth put him two ahead, although Fisher used back-to-back birdies to close out the front nine all square.
But Fisher's bogey at No. 11 allowed Westwood to get ahead for good and another bogey at the 16th gave Westwood a two-hole advantage before a birdie at the 17th clinched it.
Villegas led for most of the front nine before Singh drew even with the Colombian at the 11th. Villegas made back-to-back birdies at Nos. 13 and 14 to take control over the Indian, who appeared bothered by a foot injury.
Stenson's birdie at No. 16 provided a two-hole advantage with two to play.
Cabrera, who had curled his long birdie short to lose that hole, sent another long birdie try off the green at the 17th.
McIlroy sank a long birdie putt at the 17th before holding on for a victory, although his minus-3 hole difference will mean the 20-year-old Northern Irishman needs a big win over Stenson to advance. Westwood also needs to win big against Villegas considering his minus-4 hole ratio.
Local favorite Sergio Garcia and Martin Kaymer of Germany also meet in a meaningless Group B match.